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- Volume 50, Issue 5, 2002
Geophysical Prospecting - Volume 50, Issue 5, 2002
Volume 50, Issue 5, 2002
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Modelling and inversion of electromagnetic data using an approximate plate model
Authors Markku Pirttijärvi, Risto Pietilä, Aimo Hattula and Sven‐Erik HjeltThis paper presents a computational method for the interpretation of electromagnetic (EM) profile data in the frequency domain using a thin plate model within a two‐layer earth. The modelling method is based on an integral equation formulation, where the conductor is represented by a lattice structure composed of two‐dimensional surface elements. Several approximations are used to simplify the theoretical basis and to decrease the computation time. The simple parametric model allows efficient use of optimization methods. We employ a linearized inversion scheme based on singular value decomposition and adaptive damping. The new forward computation method and the parameter optimization are combined in the computer program, emplates. The modelling examples demonstrate that the approximate method is capable of describing the characteristic behaviour of the EM response of a thin plate‐like conductor in conductive surroundings. The efficacy of the inversion is demonstrated using both synthetic and field data. An optional depth compensation method is used to improve the interpreted values of the depth of burial. The results show that the method is cost effective and suitable for interactive interpretation of EM data.
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Experimental validation of the wavefield transform of electromagnetic fields
Authors Kaushik Das, Alex Becker and Ki Ha LeeThe wavefield transform is a mathematical technique for transforming low‐frequency electromagnetic (EM) signals to a non‐diffusive wave domain. The ray approximation is valid in the transform space and this makes traveltime tomography for 3D mapping of the electrical conductivity distribution in the subsurface possible. The transform, however, imposes stringent frequency bandwidth and signal‐to‐noise ratio requirements on the data. Here we discuss a laboratory scale experiment designed to collect transform quality EM data, and to demonstrate the practical feasibility of transforming these data to the wavefield domain.
We have used the scalable nature of EM fields to design a time‐domain experiment using graphite blocks to simulate realistic field conditions while leaving the time scale undisturbed. The spatial dimensions have been scaled down by a factor of a thousand by scaling conductivity up by a factor of a million. The graphite blocks have two holes drilled into them to carry out cross‐well and borehole‐to‐surface experiments. Steel sheets have been inserted between the blocks to simulate a conductive layer.
Our experiments show that accurate EM data can be recorded on a laboratory scale model even when the scaling of some features, such as drill‐hole diameters, is not maintained. More importantly, the time‐domain EM data recorded in cross‐well and surface‐to‐borehole modes can be usefully and accurately transformed to the wavefield domain. The observed wavefield propagation delay is proportional to the direct distance between the transmitter and receiver in a homogeneous medium. In a layered medium, data accuracy is reduced and, hence, our results are not so conclusive. On the basis of the experimental results we conclude that the wavefield transform could constitute a valid approach to the interpretation of accurate, undistorted time‐domain data if further improvement in the transform can be realized.
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Evaluation of coalbed methane reservoirs from geophysical log data using an improved fuzzy comprehensive decision method and a homologous neural network
By J. HouThe evaluation of coalbed methane reservoirs using log data is an important approach in the exploration and development of coalbed methane reservoirs. Most commonly, regression techniques, fuzzy recognition and neural networks have been used to evaluate coalbed methane reservoirs. It is known that a coalbed is an unusual reservoir. There are many difficulties in using regression methods and empirical qualitative recognition to evaluate a coalbed, but fuzzy recognition, such as the fuzzy comprehensive decision method, and neural networks, such as the back‐propagation (BP) network, are widely used. However, there are no effective methods for computing weights for the fuzzy comprehensive decision method, and the BP algorithm is a local optimization algorithm, easily trapped in local minima, which significantly affect the results. In this paper, the recognition method for coal formations is developed; the improved fuzzy comprehensive decision method, which uses an optimization approach for computing weighted coefficients, is developed for the qualitative recognition of coalbed methane reservoirs. The homologous neural network, using a homologous learning algorithm, which is a global search optimization, is presented for the quantitative analysis of parameters for coalbed methane reservoirs. The applied procedures for these methods and some problems related to their application are also discussed. Verification of the above methods is made using log data from the coalbed methane testing area in North China. The effectiveness of the methods is demonstrated by the analysis of results for real log data.
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3D free‐boundary conditions for coordinate‐transform finite‐difference seismic modelling
Authors Stig Hestholm and Bent RuudNew alternative formulations of exact boundary conditions for arbitrary three‐dimensional (3D) free‐surface topographies on seismic media have been derived. They are shown to be equivalent to previously published formulations, thereby verifying the validity of each set of formulations. The top of a curved grid represents the free‐surface topography while the interior of the grid represents the physical medium. We assume the velocity–stress version of the viscoelastic wave equations to be valid in this grid before transforming the equations to a rectangular grid. In order to perform the numerical discretization we apply the latter version of the equations for seismic wave propagation simulation in the medium. The numerical discretization of the free‐surface topography boundary conditions by second‐order finite differences (FDs) is shown, as well as the spatially unconditional stability of the resulting system of equations. The FD order is increased by two for each point away from the free surface up to eight, which is the order used in the interior. We use staggered grids in both space and time and the second‐order leap‐frog and Crank– Nicholson methods for wavefield time propagation. An application using parameters typical of teleseismic earthquakes and explosions is presented using a 200 × 100 km2 area of real topography from southwestern Norway over a homogeneous medium. A dipping plane wave simulates a teleseismic P‐wave incident on the surface topography. Results show conversion from P‐ to Rg‐ (short period fundamental mode Rayleigh) waves in the steepest and/or roughest topography, as well as attenuated waves in valleys and fjords. The codes are parallelized for simulation on fast supercomputers and PC‐clusters to model high frequencies and/or large areas.
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Seismic endoscopy: multi‐offset multi‐azimuth imaging around boreholes – data processing and experimental results
Authors Florence Nicollin, Frédéric Conil and Dominique GibertAn acoustic method, called seismic endoscopy, able to perform 3D imaging around shallow‐depth boreholes is presented. A probe, composed of an isotropic source and a directional receiver working in the 20–100 kHz frequency range, provides images of cylindrical volumes having radii of a few metres, with an accuracy of centimetres and 25° azimuthal directivity. In order to obtain clear images of the medium discontinuities, multi‐offset and multi‐azimuth data acquisition allows specific algorithms to be used to determine vertical directivity correction, azimuthal focusing and reflected wave enhancement by cancellation of the tube waves. The method is tested with data acquired in an acoustic tank and with synthetic data. Initial experimental results at a test site demonstrate the performance of the seismic endoscopy probe.
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Velocity anisotropy and attenuation of shale in under‐ and overpressured conditions
Authors Patricia Domnesteanu, Clive McCann and Jeremy SothcottThe seismic velocity and attenuation of fully saturated shales were measured for the first time under overpressured conditions, using the ultrasonic reflection technique. Shale cores from naturally overpressured horizons in the North Sea were tested in the laboratory, at confining and pore pressures relevant to in situ conditions.
A single‐frequency tone‐burst pulse wave was used to determine the seismic wave velocities and quality factors of the shale samples, with errors less than 0.3% and 0.1 dB/cm, respectively, at a frequency of 0.75 MHz. Sample length changes with varying confining and pore pressure were measured and the pore pressure equilibration time was monitored for each sample.
The anisotropy of the seismic attributes (Vp, Vs, Qp and Qs) was determined over a range of differential pressures from 5 to 60 MPa, with respect to the predominant foliation. The ultrasonic velocity data followed a transversely isotropic pattern depending on the direction of wave propagation with respect to the laminations. The Poisson's ratio was found to rise by 5% as the shale material progressed from a normally pressured to an overpressured state. The quality factor (Q) characteristics were interpreted in terms of pore geometry and connectivity as well as the directional permeability of the transversely isotropic shale material. The results were converted to bulk and shear loss modulus defects, and a positive bulk loss was observed for waves propagating perpendicular to the lamination plane even above differential pressures of 20 MPa. This indicates different levels of Biot‐flow and squirt‐flow attenuation mechanisms acting within the shale structure, depending on the wave propagation and vibration directions.
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Analysis of the resolution function in seismic prestack depth imaging
Authors L.‐J. Gelius, I. Lecomte and H. TabtiWe consider the problem of estimating subsurface quantities such as velocity or reflectivity from seismic measurements. Because of a limited aperture and band‐limited signals, the output from a seismic prestack reconstruction method is a distorted or blurred image. This distortion can be computed using the concept of resolution function, which is a quantity readily accessible in the Fourier space of the model. The key parameter is the scattering wavenumber, which at a particular image point is defined by the incident and scattered ray directions in a given background model. Any location in any background model can be considered. In general, the resolution function will depend on the following four quantities: the background velocity model, the frequency bandwidth, the wavefield type and the acquisition geometry.
We first establish the resolution function for a general scattering model assuming local reaction. We then adapt this result for two well‐known scattering models: Born and Kirchhoff. For each of these approximations the corresponding resolution function is derived and discussed. Finally, by employing a simple synthetic data example we demonstrate the ability of the resolution function to predict the image distortions.
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Towards high‐resolution 3D marine seismic surveying using Boomer sources
Authors Christof Müller, Bernd Milkereit, Thomas Bohlen and Friedrich TheilenThe use of Boomer sources for 3D seismic imaging of shallow marine structures was investigated in a feasibility study. Boomers show sufficient stability to be used in multichannel seismic surveys. The acquisition of a high‐frequency, densely sampled seismic data volume was successfully performed in the Baltic Sea. A Pleistocene fluvial channel system and shallow gas accumulations were revealed beneath the unconsolidated sediments which constitute the sea‐floor in the southern Kiel Bay.
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Uncertainties in quantitative time‐lapse seismic analysis
More LessMost seismic time‐lapse studies so far have been of a qualitative nature. Identification of areas with minor or no seismic changes has been used to plan new infill drilling targets. Increased accuracy in seismic acquisition methods, in both conventional streamer surveys and newer methods such as multicomponent sea‐bed seismic and permanent sensors, opens possibilities for the next step: quantitative time‐lapse analysis. Quantitative methods here mean the estimation of, for instance, a change in fluid saturation from 20% water to 90% water or the estimation of a pore pressure change of 5 MPa. Explicit expressions for the uncertainties associated with estimated changes in, for instance, reservoir pressure and fluid saturation are derived. These formulae can be used to compare relative uncertainties between estimated parameters as well as to identify the critical factors in various estimation techniques. The importance of accurate rock physics input, as well as that of highly repeatable time‐lapse seismic data, is emphasized. Furthermore, uncertainty analysis can be used to find optimal weight factors when the same parameter (e.g. saturation change) is estimated by two or three different techniques.
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Velocity analysis after migration
Authors Ron Silva and Yanghua WangThe double‐square‐root (DSR) equation used in pre‐stack migration is formulated in terms of velocity‐dependent and velocity‐independent terms. The velocity‐dependent term is shown to be the hyperbolic normal moveout (NMO) correction, whereas the velocity‐independent term is related to the recording geometry only. This separation of the velocity‐dependent term offers a means of applying vertical corrections to an initial migration velocity field. Using this concept, procedures are described both for velocity determination and for achieving improved structural imaging.
This decoupling is accurate both for constant‐velocity media and for media whose velocity varies as a function of depth. In media whose velocity varies as a function of both space and depth, a procedure is described for building velocity models through common‐image gather (CIG) stacking following prestack depth migration (PSDM) and time conversion (TC). This so‐called PSDM‐TC stack procedure provides a means of (a) incorporating both vertical and lateral velocity updates into an initial velocity model, (b) obtaining improved structural imaging by using a non‐optimal velocity model for the prestack depth migration, and (c) updating velocity by flattening CIGs and maximizing stack energy. The procedure can be applied to both P‐P wave and P‐SV wave migration.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 38 (1990)
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Volume 37 (1989)
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Volume 36 (1988)
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Volume 35 (1987)
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Volume 34 (1986)
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Volume 33 (1985)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 29 (1981)
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Volume 28 (1980)
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Volume 27 (1979)
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Volume 26 (1978)
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Volume 25 (1977)
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Volume 24 (1976)
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Volume 23 (1975)
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Volume 22 (1974)
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Volume 21 (1973)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 18 (1970)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 15 (1967)
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Volume 14 (1966)
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Volume 13 (1965)
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Volume 12 (1964)
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Volume 11 (1963)
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Volume 10 (1962)
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Volume 9 (1961)
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Volume 8 (1960)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 3 (1955)
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Volume 2 (1954)
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Volume 1 (1953)